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<FONT color="green">001</FONT>    package gates;<a name="line.1"></a>
<FONT color="green">002</FONT>    <a name="line.2"></a>
<FONT color="green">003</FONT>    import exceptions.noQubitException;<a name="line.3"></a>
<FONT color="green">004</FONT>    import register.Register;<a name="line.4"></a>
<FONT color="green">005</FONT>    import mathtools.*;<a name="line.5"></a>
<FONT color="green">006</FONT>    import gates.MatrixGate;<a name="line.6"></a>
<FONT color="green">007</FONT>    <a name="line.7"></a>
<FONT color="green">008</FONT>    /**<a name="line.8"></a>
<FONT color="green">009</FONT>     * &lt;p&gt;Not Gate in Matrix representation for a specified Target bit or the entire<a name="line.9"></a>
<FONT color="green">010</FONT>     * Quantum Register using target = -1 flag.&lt;br /&gt;&lt;/p&gt;<a name="line.10"></a>
<FONT color="green">011</FONT>     * <a name="line.11"></a>
<FONT color="green">012</FONT>     * &lt;p&gt;The Gate is constructed by applications of the tensor product between<a name="line.12"></a>
<FONT color="green">013</FONT>     * the 2x2 representation of Not and the 2x2 Identity Matrix. The number of<a name="line.13"></a>
<FONT color="green">014</FONT>     * applications of the tensor product is proportional to the size of the <a name="line.14"></a>
<FONT color="green">015</FONT>     * Quantum Register. For the specified target, I2 was applied to the left<a name="line.15"></a>
<FONT color="green">016</FONT>     * of Not magnitude(target) applications. I2 was applied to the right of Not<a name="line.16"></a>
<FONT color="green">017</FONT>     * (numQubits - (target+1)) applications.&lt;/p&gt;<a name="line.17"></a>
<FONT color="green">018</FONT>     * <a name="line.18"></a>
<FONT color="green">019</FONT>     * &lt;p&gt;For example a 4 Qubit Quantum Register with target 2 of Qubits(0,1,2 and 3)<a name="line.19"></a>
<FONT color="green">020</FONT>     * would be:&lt;br\&gt;<a name="line.20"></a>
<FONT color="green">021</FONT>     * notGate = I x I x Not x I&lt;br /&gt;<a name="line.21"></a>
<FONT color="green">022</FONT>     * Where x represents the Tensor Product, notGate is the construction matrix,<a name="line.22"></a>
<FONT color="green">023</FONT>     *  I is the 2x2 Identity matrix and Not is a 2x2 inversion matrix (0-&gt;1 and 1-&gt;0).&lt;/p&gt;<a name="line.23"></a>
<FONT color="green">024</FONT>     * @author Richard Inskip<a name="line.24"></a>
<FONT color="green">025</FONT>     *<a name="line.25"></a>
<FONT color="green">026</FONT>     */<a name="line.26"></a>
<FONT color="green">027</FONT>    public class NotMatrix extends MatrixGate {<a name="line.27"></a>
<FONT color="green">028</FONT>    <a name="line.28"></a>
<FONT color="green">029</FONT>            /* I2 - Identity matrix 2x2<a name="line.29"></a>
<FONT color="green">030</FONT>             * Not - 2x2 Not matrix :       |0 1|<a name="line.30"></a>
<FONT color="green">031</FONT>             *                                                      |1 0|<a name="line.31"></a>
<FONT color="green">032</FONT>             * target - the specific bit to "Not around" or flag to Not entire Register.<a name="line.32"></a>
<FONT color="green">033</FONT>             * notGate is the construction variable.<a name="line.33"></a>
<FONT color="green">034</FONT>             */<a name="line.34"></a>
<FONT color="green">035</FONT>            <a name="line.35"></a>
<FONT color="green">036</FONT>            /** Store a 2x2 identity matrix */<a name="line.36"></a>
<FONT color="green">037</FONT>            private Matrix I2 = Matrix.IdentityMatrix(2);<a name="line.37"></a>
<FONT color="green">038</FONT>            /** store a 2x2 not matrix */<a name="line.38"></a>
<FONT color="green">039</FONT>            private Matrix Not;<a name="line.39"></a>
<FONT color="green">040</FONT>            /** Store the target qubit the gate acts on*/   <a name="line.40"></a>
<FONT color="green">041</FONT>            private int target;<a name="line.41"></a>
<FONT color="green">042</FONT>            /** Matrix needed in the construction of the gate */<a name="line.42"></a>
<FONT color="green">043</FONT>            private Matrix notGate;<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>            /**<a name="line.45"></a>
<FONT color="green">046</FONT>             * Constructor. If target = -1 this will flag to Not the entire Register.<a name="line.46"></a>
<FONT color="green">047</FONT>             * @param target The target big to perform the Not gate around. <a name="line.47"></a>
<FONT color="green">048</FONT>             */<a name="line.48"></a>
<FONT color="green">049</FONT>            protected NotMatrix(int target){<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>                    // Set up variables and constant Matrices<a name="line.51"></a>
<FONT color="green">052</FONT>                    this.target = target;<a name="line.52"></a>
<FONT color="green">053</FONT>                    Complex num1 = new Complex(1.0,0.0);<a name="line.53"></a>
<FONT color="green">054</FONT>                    Not = new Matrix(2,2,0.0);<a name="line.54"></a>
<FONT color="green">055</FONT>                    Not.setElement(0,1,num1);<a name="line.55"></a>
<FONT color="green">056</FONT>                    Not.setElement(1,0,num1);<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>                    /* Begin construction of notGate depending on the value of target.<a name="line.58"></a>
<FONT color="green">059</FONT>                     * If target = 0 or -1 Not will be required on the far left of <a name="line.59"></a>
<FONT color="green">060</FONT>                     * the tensor product, therefore we set the initial variable<a name="line.60"></a>
<FONT color="green">061</FONT>                     * of notGate as Not, however, if this is not the case the first<a name="line.61"></a>
<FONT color="green">062</FONT>                     * variable will be I2, the 2x2 identity matrix.<a name="line.62"></a>
<FONT color="green">063</FONT>                     */<a name="line.63"></a>
<FONT color="green">064</FONT>                    if(target==0 || target==-1){<a name="line.64"></a>
<FONT color="green">065</FONT>                            notGate = Not;<a name="line.65"></a>
<FONT color="green">066</FONT>                    }<a name="line.66"></a>
<FONT color="green">067</FONT>                    else{<a name="line.67"></a>
<FONT color="green">068</FONT>                            notGate = I2;<a name="line.68"></a>
<FONT color="green">069</FONT>                    }<a name="line.69"></a>
<FONT color="green">070</FONT>            }<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>            /** Apply Method to apply Not Gate (Matrix) to a Quantum Register.<a name="line.72"></a>
<FONT color="green">073</FONT>             * @param r The Quantum Register<a name="line.73"></a>
<FONT color="green">074</FONT>             * @exception noQubitException If the target is outside the size of the Quantum Register throw Exception.<a name="line.74"></a>
<FONT color="green">075</FONT>             */<a name="line.75"></a>
<FONT color="green">076</FONT>            public void apply(Register r) {<a name="line.76"></a>
<FONT color="green">077</FONT>                    // Find the length of the Quantum Register<a name="line.77"></a>
<FONT color="green">078</FONT>                    int numQubits = r.getNumQbits(); <a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>                    /* Check to make sure the register is of adequate size for <a name="line.80"></a>
<FONT color="green">081</FONT>                     * the specified target. If not throw exception.<a name="line.81"></a>
<FONT color="green">082</FONT>                     */<a name="line.82"></a>
<FONT color="green">083</FONT>                    if(target&gt;(numQubits-1) || target&lt;-1){<a name="line.83"></a>
<FONT color="green">084</FONT>                            throw new noQubitException("ERROR: Target specified for Not Gate (Matrix) is not within Quantum Register.");<a name="line.84"></a>
<FONT color="green">085</FONT>                    }<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>    <a name="line.87"></a>
<FONT color="green">088</FONT>                    /* If target is -1 (flag) apply Not Gate to the entire matrix.<a name="line.88"></a>
<FONT color="green">089</FONT>                     * If target is not -1 than carry on with the remaining construction<a name="line.89"></a>
<FONT color="green">090</FONT>                     * of notGate.<a name="line.90"></a>
<FONT color="green">091</FONT>                     */<a name="line.91"></a>
<FONT color="green">092</FONT>                    if(target==-1){<a name="line.92"></a>
<FONT color="green">093</FONT>                            for(int i=1; i&lt;numQubits;i++){<a name="line.93"></a>
<FONT color="green">094</FONT>                                    notGate = notGate.tensorProduct(notGate);<a name="line.94"></a>
<FONT color="green">095</FONT>                            }<a name="line.95"></a>
<FONT color="green">096</FONT>                    }<a name="line.96"></a>
<FONT color="green">097</FONT>                    else{<a name="line.97"></a>
<FONT color="green">098</FONT>                            for(int i=1; i&lt;numQubits;i++){<a name="line.98"></a>
<FONT color="green">099</FONT>                                    if(i==target){<a name="line.99"></a>
<FONT color="green">100</FONT>                                            notGate = notGate.tensorProduct(Not);<a name="line.100"></a>
<FONT color="green">101</FONT>                                    }<a name="line.101"></a>
<FONT color="green">102</FONT>                                    else{<a name="line.102"></a>
<FONT color="green">103</FONT>                                            notGate = notGate.tensorProduct(I2);<a name="line.103"></a>
<FONT color="green">104</FONT>                                    }<a name="line.104"></a>
<FONT color="green">105</FONT>                            }<a name="line.105"></a>
<FONT color="green">106</FONT>                    }<a name="line.106"></a>
<FONT color="green">107</FONT>                    // Apply notGate to the register and then update the register.<a name="line.107"></a>
<FONT color="green">108</FONT>                    r.update(notGate.multiplyMatrix(r));<a name="line.108"></a>
<FONT color="green">109</FONT>            }<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>            /**<a name="line.111"></a>
<FONT color="green">112</FONT>             * Return the name of the Gate.<a name="line.112"></a>
<FONT color="green">113</FONT>             */<a name="line.113"></a>
<FONT color="green">114</FONT>            public String getName() {<a name="line.114"></a>
<FONT color="green">115</FONT>                    return "Not";<a name="line.115"></a>
<FONT color="green">116</FONT>            }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>    }<a name="line.118"></a>




























































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